Histopolating splines (Q939570)

This paper studies the problem of histopolation or piecewise area matching to a given function. A general procedure is proposed in order to construct a spline solution of degree \(n\) with prescribed knots, such that polynomials of degree \(n\) are reproduced and the corresponding fundamental functions are compactly supported. In the case of equidistant knot sequences, it is shown that the fundamental histosplines are translates of a fixed function. The general method is illustrated with two types of histopolating splines: one based on the nodal splines of J.M. de Villiers and C.H. Rohwer, the other on a spline operator introduced by D.X. Qi.